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1.
We consider analytic vacuum and electrovacuum spacetimes which contain a compact null hypersurface ruled byclosed null generators. We prove that each such spacetime has a non-trivial Killing symmetry. We distinguish two classes of null surfaces, degenerate and non-degenerate ones, characterized by the zero or non-zero value of a constant analogous to the “surface gravity” of stationary black holes. We show that the non-degenerate null surfaces are always Cauchy horizons across which the Killing fields change from spacelike (in the globally hyperbolic regions) to timelike (in the acausal, analytic extensions). For the special case of a null surface diffeomorphic toT 3 we characterize the degenerate vacuum solutions completely. These consist of an infinite dimensional family of “plane wave” spacetimes which are entirely foliated by compact null surfaces. Previous work by one of us has shown that, when one dimensional Killing symmetries are allowed, then infinite dimensional families of non-degenerate, vacuum solutions exist. We recall these results for the case of Cauchy horizons diffeomorphic toT 3 and prove the generality of the previously constructed non-degenerate solutions. We briefly discuss the possibility of removing the assumptions of closed generators and analyticity and proving an appropriate generalization of our main results. Such a generalization would provide strong support for the cosmic censorship conjecture by showing that causality violating, cosmological solutions of Einstein's equations are essentially an artefact of symmetry. 相似文献
2.
Vincent Moncrief 《Journal of Geometry and Physics》1984,1(1):107-130
In this paper we show how to construct all analytic solutions of the vacuum Einstein equations having a compact Cauchy horizon diffeomorphic to S3 and ruled by closed null generators which fiber the horizon in the sense of Hopf. The set of (inequivalent) solutions is infinite dimensional, contains the two parameter Taub-NUT family as a special case, and may be uniquely parameterized by a pair of arbitrary, real analytic functions on S2 (modulo an action of the conformal group of S2). The horizon of each such solution is necessarily a Killing horizon (as proven recently by Isenberg and the author) and is shown here always to be a «crushingå horizon in the sense of Eardley and Smarr. Some recent results of Gerhardt are used to show that a neighborhood of the horizon (in the globally hyperbolic region) is always foliated by constant mean curvature hypersurfaces.The possible isometry groups of the solutions considered are characterized in terms of isometries of the determining «Cauchy dataå which is specified on the horizons themselves. 相似文献
3.
It is a well known analytic result in general relativity that the 2-dimensional area of the apparent horizon of a black hole
remains invariant regardless of the motion of the observer, and in fact is independent of the t = constant slice, which can be quite arbitrary in general relativity. Nonetheless the explicit computation of horizon area is often
substantially more difficult in some frames (complicated by the coordinate form of the metric), than in other frames. Here
we give an explicit demonstration for very restricted metric forms of (Schwarzschild and Kerr) vacuum black holes. In the
Kerr–Schild coordinate expression for these spacetimes they have an explicit Lorentz-invariant form. We consider boosted versions with the black hole moving through the coordinate system. Since these are stationary black hole spacetimes, the
apparent horizons are two dimensional cross sections of their event horizons, so we compute the areas of apparent horizons
in the boosted space with (boosted) t = constant, and obtain the same result as in the unboosted case. Note that while the invariance of area is generic, we deal only with
black holes in the Kerr–Schild form, and consider only one particularly simple change of slicing which amounts to a boost.
Even with these restrictions we find that the results illuminate the physics of the horizon as a null surface and provide
a useful pedagogical tool. As far as we can determine, this is the first explicit calculation of this type demonstrating the
area invariance of horizons. Further, these calculations are directly relevant to transformations that arise in computational
representation of moving black holes. We present an application of this result to initial data for boosted black holes. 相似文献
4.
Hawking’s theorem on the topology of black holes asserts that cross sections of the event horizon in 4-dimensional asymptotically flat stationary black hole spacetimes obeying the dominant energy condition are topologically 2-spheres. This conclusion extends to outer apparent horizons in spacetimes that are not necessarily stationary. In this paper we obtain a natural generalization of Hawking’s results to higher dimensions by showing that cross sections of the event horizon (in the stationary case) and outer apparent horizons (in the general case) are of positive Yamabe type, i.e., admit metrics of positive scalar curvature. This implies many well-known restrictions on the topology, and is consistent with recent examples of five dimensional stationary black hole spacetimes with horizon topology S
2 × S
1. The proof is inspired by previous work of Schoen and Yau on the existence of solutions to the Jang equation (but does not make direct use of that equation). 相似文献
5.
Tevian Dray Ravi Kulkarni Corinne A. Manogue 《General Relativity and Gravitation》1992,24(12):1255-1266
A quantization procedure is given for the scalar field on stationary, axisymmetric background spacetimes with orthogonal 2-surfaces.
The procedure is based on observers orthogonal to surfaces of constant Killing time, and thus agrees with the usual procedure
for static spacetimes. For stationary but nonstatic spacetimes the procedure differs from the usual one but nonetheless leads
to a natural quantization scheme. Applying the procedure to flat space in rotating coordinates gives the standard, inertial
Minkowski vacuum. For the Kerr spacetime, the procedure yields a particle definition which is well-defined everywhere outside
the horizon. The above observers are just nonrotating ZAMO's, and the vacuum state smoothly interpolates between the “in”
and “out” Boulware vacua. 相似文献
6.
We study the mode solution to the Cauchy problem of the scalar wave equation □φ = 0 in Kasner spacetimes. As a first result, we give the explicit mode solution in axisymmetric Kasner spacetimes, of which flat Kasner spacetimes are special cases. Furthermore, we give the small and large time asymptotics of the modes in general Kasner spacetimes. Generically, the modes in non-flat Kasner spacetimes grow logarithmically for small times, while the modes in flat Kasner spacetimes stay bounded for small times. For large times, however, the modes in general Kasner spacetimes oscillate with a polynomially decreasing amplitude. This gives a notion of large time frequency of the modes, which we use to model the wavelength of light rays in Kasner spacetimes. We show that the redshift one obtains in this way actually coincides with the usual cosmological redshift. 相似文献
7.
Motivated in part by Eardley et al. (Commun Math Phys 106(1):137–158, 1986), in this note we obtain a rigidity result for globally hyperbolic vacuum spacetimes in arbitrary dimension that admit a timelike conformal Killing vector field. Specifically, we show that if M is a Ricci flat, timelike geodesically complete spacetime with compact Cauchy surfaces that admits a timelike conformal Killing field X, then M must split as a metric product, and X must be Killing. This gives a partial proof of the Bartnik splitting conjecture in the vacuum setting. 相似文献
8.
9.
John K. Beem 《General Relativity and Gravitation》1995,27(1):93-108
LetS be a partial Cauchy surface for (M, go) which remains a partial Cauchy surface under small metric perturbations. In general, the Cauchy horizon H+(go, S) may be unstable to small changes in the metric. Points of the horizon may move by large amounts and even the topological type of the horizon may change under arbitrarily small changes in the metric tensor. In this paper, we investigate sufficient conditions for existential, locational, and topological stability of Cauchy horizons under metric changes which perturb the light cones by small amounts. 相似文献
10.
Stefan Hollands 《Communications in Mathematical Physics》2001,216(3):635-661
We characterise the homogeneous and isotropic gauge invariant and quasifree states for free Dirac quantum fields on Robertson–Walker
spacetimes. Using this characterisation, we construct adiabatic vacuum states of order n corresponding to some Cauchy surface. It is demonstrated that any two such states (of sufficiently high order) are locally
quasi-equivalent. We give a microlocal characterisation of spinor Hadamard states and we show that this agrees with the usual
characterisation of such states in terms of the singular behaviour of their associated twopoint functions. The polarisation
set of these twopoint functions is determined and found to have a natural geometric form. We finally prove that our adiabatic
states of infinite order are Hadamard, and that those of order n correspond, in some sense, to a truncated Hadamard series and therefore allow for a point splitting renormalisation of the
expected stress-energy tensor.
Received: 30 June 1999 / Accepted: 21 September 2000 相似文献
11.
Stefanos Aretakis 《Communications in Mathematical Physics》2011,307(1):17-63
We study the problem of stability and instability of extreme Reissner-Nordström spacetimes for linear scalar perturbations. Specifically, we consider solutions to the linear wave equation \({\square_{g}\psi=0}\) on a suitable globally hyperbolic subset of such a spacetime, arising from regular initial data prescribed on a Cauchy hypersurface Σ0 crossing the future event horizon \({\mathcal{H}^{+}}\) . We obtain boundedness, decay and non-decay results. Our estimates hold up to and including the horizon \({\mathcal{H}^{+}}\) . The fundamental new aspect of this problem is the degeneracy of the redshift on \({\mathcal{H}^{+}}\) . Several new analytical features of degenerate horizons are also presented. 相似文献
12.
I. Caprini 《Nuclear Physics B》1974,68(2):561-573
A method for determining high-energy parameters from low-energy data is described and applied to the πN forward charge-exchange amplitude A′(?). Unlike the usual FESR or CMSR which are based upon the Cauchy integral formula (dispersion relations) the present method used the solution of an extremal problem in the space of analytic functions. This allows us to derive in a completely model independent way optimal bounds on Regge residues and correlations between Regge parameters and low-energy data. 相似文献
13.
14.
For near horizon geometry we examine the linearized equations around extremal Kerr horizon (which is a unique axially symmetric near horizon geometry) and give some arguments towards stability of this horizon with respect to generic (non-symmetric) linear perturbation of near horizon geometry. The result is also applicable for other situations like Kundt’s class spacetimes or isolated horizons. 相似文献
15.
Geoffrey L Sewell 《Annals of Physics》1982,141(2):201-224
We formulate an axiomatic scheme, designed to provide a framework for a general, rigorous theory of relativistic quantum fields on a class of manifolds, that includes Kruskal's extension of Schwarzschild space-time, as well as Minkowski space-time. The scheme is an adaptation of Wightman's to this class of manifolds. We infer from it that, given an arbitrary field (in general, interacting) on a manifold X, the restriction of the field to a certain open submanifold X(+), whose boundaries are event horizons, satisfies the Kubo-Martin-Schwinger (KMS) thermal equilibrium conditions. This amounts to a rigorous, model-independent proof of a generalised Hawking-Unruh effect. Further, in cases where the field enjoys a certain PCT symmetry, the conjugation governing the KMS condition is just the PCT operator. The key to these results is an analogue, that we prove, of the Bisognano-Wichmann theorem. [J. Math. Phys.17 (1976), Theorem 1]. We also construct an alternative scheme by replacing a regularity condition at an event horizon by the assumption that the field in X(+) is in a ground, rather than a thermal, state. We show that, in this case, the observables in X(+) are uncorrelated to those in its causal complement, X(?), and thus that the event horizons act as physical barriers. Finally, we argue that the choice between the two schemes must be dictated by the prevailing conditions governing the state of the field. 相似文献
16.
We first review the accelerating, rotating and charged Plebanski–Demianski (PD) black hole, which includes the Kerr–Newman rotating black hole and the Taub-NUT spacetime. The main feature of this black hole is that it has 4 horizons like event horizon, Cauchy horizon and two accelerating horizons. In the non-extremal case, the surface area, entropy, surface gravity, temperature, angular velocity, Komar energy and irreducible mass on the event horizon and Cauchy horizon are presented for PD black hole. The entropy product, temperature product, Komar energy product and irreducible mass product have been found for event horizon and Cauchy horizon. Also their sums are found for both horizons. All these relations are dependent on the mass of the PD black hole and other parameters. So all the products are not universal for PD black hole. The entropy and area bounds for two horizons have been investigated. Also we found the Christodoulou–Ruffini mass for extremal PD black hole. Finally, using first law of thermodynamics, we also found the Smarr relation for PD black hole. 相似文献
17.
18.
Helmut Friedrich István Rácz Robert M. Wald 《Communications in Mathematical Physics》1999,204(3):691-707
We consider smooth electrovac spacetimes which represent either (A) an asymptotically flat, stationary black hole or (B) a
cosmological spacetime with a compact Cauchy horizon ruled by closed null geodesics. The black hole event horizon or, respectively,
the compact Cauchy horizon of these spacetimes is assumed to be a smooth null hypersurface which is non-degenerate in the
sense that its null geodesic generators are geodesically incomplete in one direction. In both cases, it is shown that there
exists a Killing vector field in a one-sided neighborhood of the horizon which is normal to the horizon. We thereby generalize
theorems of Hawking (for case (A)) and Isenberg and Moncrief (for case (B)) to the non-analytic case.
Received: 4 November 1998 / Accepted: 13 February 1999 相似文献
19.
Vincent E. Moncrief 《General Relativity and Gravitation》1983,15(4):309-314
The cosmic censorship conjecture states that naked singularities should not evolve from regular initial conditions in general relativity. In its strong form the conjecture asserts that space-times with Cauchy horizons must always be unstable and thus that thegeneric solution of Einstein's equations must be inextendible beyond its maximal Cauchy development. In this paper we shall show that one can construct an infinite-dimensional family ofextendible cosmological solutions similar to Taub-NUT space-time. However, we shall also show that each of these solutions is unstable in precisely the way demanded by strong cosmic censorship. Finally we show that quantum fluctuations in the metric always provide (though in an unexpectedly subtle way) the “generic perturbations” which destroy the Cauchy horizons in these models. 相似文献
20.
T. Padmanabhan 《General Relativity and Gravitation》2002,34(12):2029-2035
I provide a general proof of the conjecture that one can attribute an entropy to the area of any horizon. This is done by constructing a canonical ensemble of a subclass of spacetimes with a fixed value for the temperature T = –1 and evaluating the exact partition function Z(). For spherically symmetric spacetimes with a horizon at r = a, the partition function has the generic form Z exp[S – E], where S = (1/4)4 a
2 and |E| = (a/2). Both S and E are determined entirely by the properties of the metric near the horizon. This analysis reproduces the conventional result for the black-hole spacetimes and provides a simple and consistent interpretation of entropy and energy for De Sitter spacetime. For the Rindler spacetime the entropy per unit transverse area turns out to be (1/4) while the energy is zero. Further, I show that the relationship between entropy and area allows one to construct the action for the gravitational field on the bulk and thus the full theory. In this sense, gravity is intrinsically holographic. 相似文献