Related papers: Never Judge a Black Hole by Its Area
Classically, black holes admit maximal interior volumes that grow asymptotically linearly in time. We show that such volumes remain large when Hawking evaporation is taken into account. Even if a charged black hole approaches the extremal…
The information loss paradox is often discussed from the perspective of the observers who stay outside of a black hole. However, the interior spacetime of a black hole can be rather nontrivial. We discuss the open problems regarding the…
The interior volume of black holes as defined by Christodoulou and Rovelli exhibits many surprising features. For example, it increases with time, even under Hawking evaporation. For some black holes, the interior volume is not even a…
The 3d volume inside a spherical black hole can be defined by extending an intrinsic flat-spacetime characterization of the volume inside a 2-sphere. For a collapsed object, the volume grows with time since the collapse, reaching a simple…
Christodoulou and Rovelli have remarked on the large interiors possessed by static black holes. We amplify their remarks, and extend them to the spinning case.
Christodoulou and Rovelli have calculated maximal interior volume of a Schwarzschild black hole which linearly grows with time. Recently, the entropy of interior volume in a Schwarzschild black hole has also been calculated. In this…
The basic and conceptual notion of this work starts from the recent investigations of Marios Christodoulou and Carlo Rovelli (CR) in their paper entitled ''How big is a black hole?''. This work is related to the black hole interior volume…
Christodoulou and Rovelli have shown that the maximal interior volume of a Schwarzschild black hole linearly grows with time. Recently, their conclusion has been extended to the Reissner{-}Nordstr$\ddot{\text{o}}$m and Kerr black holes.…
Black holes that have nearly evaporated are often thought of as small objects, due to their tiny exterior area. However, the horizon bounds large spacelike hypersurfaces. A compelling geometric perspective on the evolution of the interior…
The presumption that Hawking radiations are thermally distributed can be considered to result from their entanglement with the internal degrees of freedom for a black hole. This leads to the "firewall" paradox if unitary evolution continues…
The investigation about the volume of a black hole is closely related to the quantum nature of the black hole. The entropy is a significant concept for this. A recent work by Majhi and Samanta [Phys. Lett. B 770 (2017) 314] after us…
Using black-hole arguments with widely accepted premises, we show that it is extremely improbable that space is Euclidean, and that it is unspeakably improbable that space is hyperbolic. Independently, using an argument which makes no…
The horizon (the surface) of a black hole is a null surface, defined by those hypothetical "outgoing" light rays that just hover under the influence of the strong gravity at the surface. Because the light rays are orthogonal to the spatial…
This paper reviews the work done on black hole interior volume, entropy, and evaporation. An insight into the basics for understanding the interior volume is presented. A general analogy to investigate the interior volume of a black hole,…
Based on an investigation into the near-horizon geometrical description of black hole spacetimes (the so-called "($r$,$t$) sector"), we find that the surface area of the event horizon of a black hole is mirrored in the area of a…
We discuss the limitations on space time measurement in the Schwarzchild metric. We find that near the horizon the limitations on space time measurement are of the order of the black hole radius. We suggest that it indicates that a large…
The information loss paradox is often presented as an unavoidable consequence of well-established physics. However, in order for a genuine paradox to ensue, not-trivial assumptions about, e.g., quantum effects on spacetime, are necessary.…
It is shown that an exactly static and spherically symmetric black hole event horizon cannot be embedded in a time-dependent geometry. Forcing it to do so results in a naked null singularity at the would-be horizon. Therefore, since the…
The black hole information paradox is related to the area of event horizon, and potentially to the volume and singularity behind it. One example is the complexity/volume duality conjectured by Stanford and Susskind. Accepting the proposal…
Understanding the fate of semi-classical black hole solutions at very late times is one of the most important open questions in quantum gravity. In this paper, we provide a path integral definition of the volume of the black hole interior…