Black and White Hole Twins Connected by Quantum Gravity

By Javier Olmedo, Sahil Saini and Parampreet Singh

Black holes are perhaps the most exotic objects in our Universe with very intriguing properties. The event horizon does not allow light and matter to escape, and hides the central singularity. As in the case of the big bang singularity, the central singularity is a strong curvature singularity where all in-falling objects are annihilated irrespective of their strength. Since singularities point out pathologies of general relativity, a more fundamental description obtained from quantum gravity must resolve the problem of singularities. Singularity resolution is also important for resolving many of the paradoxes and conundrums that plague the classical theory such as the cosmic censorship conjecture, black hole evaporation, black hole information loss paradox, etc.

Black holes have mirror versions too. Known as white holes, these are solutions of general relativity with the same spacetime metric.  If the black holes do not allow even the light to escape once it enters the horizon, thus nothing can enter the white hole horizon. Light and matter can only escape from the white hole. It has sometimes been speculated that black hole and white hole solutions can be connected, providing gateways between different universes or travelling within the same universe, but details have been sparse. The reason is due to the presence of the central singularity which does not allow a bridge between the black and white holes.

It has been long hoped that the knowledge of non-perturbative quantum gravitational effects can result in insights on the resolution of singularities such as inside the black holes. Over the last decade, progress in loop quantum gravity has been quite promising on this frontier. Rigorous quantizations of cosmological and black hole spacetimes have been performed and effects of quantum geometry have been understood in detail. These directly translate to upper bounds on the spacetime curvature and lead to resolution of singularities. In the cosmological spacetimes, extensive numerical simulations show that the big bang is replaced by a big bounce [1]. The fate of the central singularity in black hole spacetimes has been hoped to be of the same nature.

In this manuscript, authors study the singularity resolution in the interior of a Schwarzschild black hole using techniques of loop quantum gravity. Earlier work on this showed that the central singularity is resolved and a white hole forms, albeit with a mass which is much larger than the mass of black hole [2]. In fact, the mass of the white hole turns out to be a quartic power of the black hole mass. One of main questions which is answered in the manuscript is whether quantum gravity allows a bounce where masses of black and white holes are similar. Note that the central singularity is dictated by the Weyl curvature, and hence the spacetime near the singularity is highly anisotropic. Therefore, obtaining a symmetric bounce is a non-trivial requirement in a gravitational collapse.  Authors show by utilising certain freedom in the quantum theory, it is possible to resolve the singularity and achieve a symmetric bounce. Three different families of solutions are studied which yield a symmetric bounce.  In such a symmetric bounce, black and white holes have identical masses. They are essentially twins separated by a small quantum gravitational bridge through which a non-singular evolution takes place.

From black holes to white holes_2017

The figure shows the Penrose-Carter diagram of the black hole to white hole transition for a hypothetical observer falling in to the black hole, passing the quantum gravity regime and coming through the white hole horizon. The transition is non-singular, thanks to the non-perturbative quantum gravity effects.

The picture of the spacetime seen by an observer in this black hole to white hole transition is the following. Free falling observers entering in the black holes do not experience anything special. It is only when they reach the quantum region of the spacetime when they will experience high (but finite) curvature. However, unlike the classical theory, they do not see evolution to stop. The singularity is avoided and they experience a decrease in the curvature of their spacetime. This is interpreted as a quantum bounce through which the interior of a black hole is connected to the interior of a white hole on the other side. Observers will exit this spacetime through the white hole horizon, characterised by a mass that is exactly the same as the mass of the black hole they fell in.

Interestingly, these results are supported by complementary studies about the quantization of full vacuum spherically symmetric spacetimes [3]. Further, these results can provide an evidence for a symmetric bounce often conjectured in phenomenological studies of black hole to white hole transitions [4]. It remains to be seen whether loop quantum effects as studied in this manuscript can leave any phenomenological signatures.

The manuscript “From black holes to white holes: a quantum gravitational, symmetric bounce” is published in Classical and Quantum Gravity, Vol 34, 225011 (2017)


[1] A. Ashtekar, P. Singh, Loop Quantum Cosmology: A Status Report, Class. Quant. Grav. 28 (2011) 213001

[2] A. Corichi, P. Singh, Loop quantization of the Schwarzschild interior revisited, Class. Quantum Grav. 33 (2016) 055006.

[3]  J. Olmedo, Brief review on black hole loop quantization, Universe 2, 12 (2016).

[4]  A. Barrau, C. Rovelli, F. Vidotto, Fast radio bursts and white hole signals, Phys. Rev. D 90, 127503 (2014)

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