Conformal scalar propagation on the Schwarzschild black-hole geometry

The vacuum activity generated by the curvature of the Schwarzschild black-hole geometry close to the event horizon is studied for the case of a massless, conformal scalar field. The associated approximation to the unknown, exact propagator in the Hartle–Hawking vacuum state for small values of the radial coordinate above r = 2M results in an analytic expression which manifestly features its dependence on the background space–time geometry. This approximation to the Hartle–Hawking scalar propagator on the Schwarzschild black-hole geometry is, for that matter, distinct from all other. It is shown that the stated approximation is valid for physical distances which range from the event horizon to values which are orders of magnitude above the scale within which quantum and backreaction effects are comparatively pronounced. An expression is obtained for the renormalised \({ \langle\phi^2(x)\rangle}\) in the Hartle–Hawking vacuum state which reproduces the established results on the event horizon and in that segment of the exterior geometry within which the approximation is valid. In contrast to previous results the stated expression has the superior feature of being entirely analytic. The effect of the manifold’s causal structure to scalar propagation is also studied.     

Conformal structure of a Schwarzschild black hole immersed in a Friedman universe

The evolution of a Schwarzschild black hole in an expanding Friedman universe is described using the same coordinate patch for both geometries. Comoving and extended Kruskal coordinates are considered and compared for the casesk=0 andk=1. The conformal structure and some global topological aspects of the Schwarzschild-Friedman system are examined with the help of diagrams in comoving and extended Kruskal coordinates.     

Wave dynamics of phantom scalar perturbation in the background of Schwarzschild black hole

Using Leaver's continue fraction and time domain method, we investigate the wave dynamics of phantom scalar perturbation in the background of Schwarzschild black hole. We find that the presence of the negative kinetic energy terms modifies the standard results in quasinormal spectrums and late-time behaviors of the scalar perturbations. The phantom scalar perturbation in the late-time evolution will grow with an exponential rate.     

Absorption of massless scalar wave from Schwarzschild black hole surrounded by quintessence

By using the partial wave method, we investigate the absorption of massless scalar wave from Schwarzschild black hole surrounded by the quintessence. We obtained the expression of absorption cross section
080402
Then we numerically carry out the absorption cross section and we find that the larger angular momentum quantum number l is, the smaller the corresponding maximum value of partial absorption cross section is, and that the total absorption cross section tends to geometric-optical limit σ_abs^hf≈ π b_c². We also find that higher value of ω_q (state parameter of the quintessence) corresponds the higher value of absorption cross section σ_abs.     

Massive scalar field quasinormal modes of a Schwarzschild black hole surrounded by quintessence

We present the quasinormal frequencies of the massive scalar field in the background of a Schwarzchild black hole surrounded by quintessence with the third-order WKB method. The mass of the scalar field u plays an important role in studying the quasinormal frequencies, the real part of the frequencies increases linearly as mass of the field u increases, while the imaginary part in absolute value decreases linearly which leads to damping more slowly than the massless scalar field. The frequencies have a limited value, so it is easier to detect the quasinormal modes. Moreover, owing to the presence of the quintessence, the massive scalar field damps more slowly.      

Absorption of a massless scalar wave from a Schwarzschild black hole surrounded by quintessence

By using the partial wave method,we investigate the absorption of a massless scalar wave from a Schwarzschild black hole surrounded by quintessence.We obtained the expression of absorption cross section σabs(ω)=π/ω2sum from l=0 to ∞(2l+1)|Tωl(ω)|2=π/ω2sum from l=0 to ∞(2l+1)Γωl(ω).Then we numerically carry out the absorption cross section and we find that the larger the angular momentum quantum number l is,the smaller the corresponding maximum value of the partial absorption cross section is,and that the total absorption cross section tends to the geometric-optical limit σ hf abs ≈πb 2 c.We also find that higher value of ω q(state parameter of quintessence) corresponds to the higher value of absorption cross section σ abs.     

Un-graviton corrections to the Schwarzschild black hole

We introduce an effective action smoothly extending the standard Einstein–Hilbert action to include un-gravity effects. The improved field equations are solved for the un-graviton corrected Schwarzschild geometry reproducing the Mureika result. This is an important test to confirm the original “guess” of the form of the un-Schwarzschild metric. Instead of working in the weak field approximation and “dressing” the Newtonian potential with un-gravitons, we solve the “effective Einstein equations” including all order un-gravity effects. An unexpected “bonus” of accounting un-gravity effects is the fractalisation   of the event horizon. In the un-gravity dominated regime the event horizon thermodynamically behaves as fractal surface of dimensionality twice the scale dimension dU$d_U$.     

Falling into a Schwarzschild black hole

Consider a radially freely falling observer who plunges into a Schwarzschild black hole. In contrast to a static observer, he will have a different view of the black hole and of the outer sky. Furthermore, the relationship between the proper time of the falling observer and the proper time of a distant static observer differs from the relationship between the proper times of two static observers or two freely falling observers.     

Schwarzschild black hole in noncommutative spaces

We study the effects of noncommutative spaces on the horizon, the area spectrum and Hawking temperature of a Schwarzschild black hole. The results show deviations from the usual horizon, area spectrum and the Hawking temperature. The deviations depend on the parameter of space/space noncommutativity.     

Conformal scalar propagation and Hawking radiation

The construction of the conformal scalar propagator which has been obtained in the preceding two projects as an analytic function of the Schwarzschild black-hole space-time is completed with a boundary condition imposed by the physical context through contour integration in the exterior vicinity of the event horizon. It is shown that, as a consequence of the semi-classical character which the emitted quanta have in that exterior vicinity, the particle production by the Schwarzschild black hole which was formally established in the preceding project is identical to thermal Hawking radiation. By extension, it is established that such a particle production corresponds to a spectrum which detracts from thermality by the amount predicted by Parikh and Wilczek if energy conservation is properly imposed as a constraint on scalar propagation. The results obtained herein support the case made by Hawking on the relation between quantum propagation and observation of particles produced by a black hole.     

Phase transition of quantum-corrected Schwarzschild black hole

We study the thermodynamic phase transition of a quantum-corrected Schwarzschild black hole. The modified metric affects the critical temperature which is slightly less than the conventional one. The space without black holes is not the hot flat space but the hot curved space due to vacuum fluctuations so that there appears a type of Gross–Perry–Yaffe phase transition even for the very small size of black hole, which is impossible for the thermodynamics of the conventional Schwarzschild black hole. We discuss physical consequences of the new phase transition in this framework.     

量子史瓦茨黑洞和暗物质

引入Sommerfeld作用量量子化条件来处理Schwarzschild黑洞的量子化问题. 发现此类量子化黑洞存在一个质量为m_G=123m_p的基态，处于基态的量子Schwarzschild黑洞不再存在Hawking蒸发和任何其他辐射，可名之曰暗星. 它的存在不仅可以解决信息丢失的疑难，而且极可能是构成暗物质的主要候选者. 关键词： 量子史瓦茨黑洞 暗物质     

Statistical entropy of a Schwarzschild black hole

A model describing the internal microstates of particles is used to calculate the statistical entropy of a Schwarzschild black hole. The state of the system is described by a nonextensive entropy function which is superadditive and so fails to be concave. A strict maximum of the entropy does not exist; nonetheless, the entropy increases on merging two such systems.     

Schwarzschild black hole with global monopole charge

We derive the metric for a Schwarzschild black hole with global monopole charge by relaxing asymptotic flatness of the Schwarzschild field. We then study the effect of global monopole charge on particle orbits and the Hawking radiation. It turns out that existence, boundedness and stability of circular orbits scale up by (1−8πη ²)⁻¹, and the perihelion shift and the light bending by (1−8πη ²)^−3/2, while the Hawking temperature scales down by (1−8πη ²)² the Schwarzschild values. Hereη is the global charge.     

Isotropic coordinates for Schwarzschild black hole radiation

The isotropic coordinate system of Schwarzschild spacetime has several attractive properties similar with the Painlevé–Gullstrand coordinates. The purpose for us to choose the isotropic coordinates is to resolve the ambiguities of the tunneling picture in Hawking radiation. Based on energy conservation, we investigate Hawking radiation as massless particles tunneling across the event horizon of the Schwarzschild black hole in the isotropic coordinates. Because the amplitude for a black hole to emit particles is related to the amplitude for it to absorb, we must take into account the contribution of ingoing solution to the action, ImS=ImS_out−ImS_in. It will be shown that the imaginary part of action for ingoing particles is zero (ImS_in=0) in the Painlevé–Gullstrand coordinates, so the equation ImS=ImS_out−ImS_in is valid in both the isotropic coordinates and the Painlevé–Gullstrand coordinates.