Interior volume of (1 + D)-dimensional Schwarzschild black hole

Abstract

We calculate the maximum interior volume, enclosed by the event horizon, of a (1 + D)dimensional Schwarzschild black hole. Taking into account the mass change due to Hawking radiation, we show that the volume increases towards the end of the evaporation. This fact is not new as it has been observed earlier for four dimensional case. The interesting point we observe is that this increase rate decreases towards the higher value of space dimensions D; i.e. it is a decelerated expansion of volume with the increase of spacial dimensions. This implies that for a sufficiently large D, the maximum interior volume does not change. The possible implications of these results are also discussed. *

Interior volume of Banados–Teitelboim–Zanelli black hole

“…However, more numerical technologies should be used to solve the equations of motion and we do not plan to conduct it here. In terms of physical significance, firstly, we extend the concept of interior volume to lower spacetime dimensions, comparing to those in higher dimensions [10,17].…”

“…The horizon of a spherically symmetric black hole is foliated by spacelike spheres S v labelled by the asymptotic time v while the sphere S v is defined as the one crossed by a light signal sent by a remote stationary observer at position r with proper time t = v − r. The maximal volume of the spherically symmetric surface Σ bounded by S v is the so-called CR volume. It was shown that the interior volumes grow with time for the Schwarzschild black hole [9,10], Reissner-Nordström (RN) black hole [9,11], Kerr black hole [12,13]. These results as well as the analysis of entropy of massless scalar particles inside the black holes [14,15] may provide us with implications on discussions of the information paradox, since a larger and larger volume can accommodate huger and huger information [16].…”

On horizonless temperature with an accelerating mirror

“…It was suggested in [28] that the corresponding black hole picture might be a black hole remnant [30,31], and that unitarity is maintained in the sense that if one takes into account both the exterior and the interior of a black hole, then the entire quantum state is pure at all times. In such a picture, information remains hidden inside the ever-shrinking black hole horizon (the interior spacetime can still have a large volume [21,[31][32][33][34][35][36], see however [37]) and the radiation is never purified. Since the end state is a remnant, the information inside is never destroyed 4 .…”

Information evolution in the interior of an axially symmetric BTZ black hole

“…( 13), one can get the maximal interior volume form Eq. (12). Which shows that the interior volume of BTZ black hole is proportional to advance time.…”

“…Along this way, many authors defined the interior volume of different black holes for D ≥ 4 [10][11][12][13][15][16][17]. In all these analysis the interior volumes of black hole is found directly increasing with advance time v. Based on CR work, Baocheng Zhang [18,19] considered the interior quantum modes of scalar field and investigated the entropy inside the black hole as…”