QUANTUM gravitational effects are usually ignored in calculations of the formation and evolution of black holes. The justification for this is that the radius of curvature of space-time outside the event horizon is very large compared to the Planck length (Għ/c3)1/2 ≈ 10−33 cm, the length scale on which quantum fluctuations of the metric are expected to be of order unity. This means that the energy density of particles created by the gravitational field is small compared to the space-time curvature. Even though quantum effects may be small locally, they may still, however, add up to produce a significant effect over the lifetime of the Universe ≈ 1017 s which is very long compared to the Planck time ≈ 10−43 s. The purpose of this letter is to show that this indeed may be the case: it seems that any black hole will create and emit particles such as neutrinos or photons at just the rate that one would expect if the black hole was a body with a temperature of (κ/2π) (ħ/2k) ≈ 10−6 (M/M)K where κ is the surface gravity of the black hole1. As a black hole emits this thermal radiation one would expect it to lose mass. This in turn would increase the surface gravity and so increase the rate of emission. The black hole would therefore have a finite life of the order of 1071 (M/M)−3 s. For a black hole of solar mass this is much longer than the age of the Universe. There might, however, be much smaller black holes which were formed by fluctuations in the early Universe2. Any such black hole of mass less than 1015 g would have evaporated by now. Near the end of its life the rate of emission would be very high and about 1030 erg would be released in the last 0.1 s. This is a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1 Mton hydrogen bombs. It is often said that nothing can escape from a black hole. But in 1974, Stephen Hawking realized that, owing to quantum effects, black holes should emit particles with a thermal distribution of energies — as if the black hole had a temperature inversely proportional to its mass. In addition to putting black-hole thermodynamics on a firmer footing, this discovery led Hawking to postulate 'black hole explosions', as primordial black holes end their lives in an accelerating release of energy.

Black Hole Explosions

When all thermonuclear sources of energy are exhausted a sufficiently heavy star will collapse. Unless fission due to rotation, the radiation of mass, or the blowing off of mass by radiation, reduce the star's mass to the order of that of the sun, this contraction will continue indefinitely. In the present paper we study the solutions of the gravitational field equations which describe this process. In I, general and qualitative arguments are given on the behavior of the metrical tensor as the contraction progresses: the radius of the star approaches asymptotically its gravitational radius; light from the surface of the star is progressively reddened, and can escape over a progressively narrower range of angles. In II, an analytic solution of the field equations confirming these general arguments is obtained for the case that the pressure within the star can be neglected. The total time of collapse for an observer comoving with the stellar matter is finite, and for this idealized case and typical stellar masses, of the order of a day; an external observer sees the star asymptotically shrinking to its gravitational radius.

On Continued Gravitational Contraction

How the Laws of Physics Lie

According to an adequacy-for-purpose view, models should be assessed with respect to their adequacy or fitness for particular purposes. Such a view has been advocated by scientists and philosophers...

https://www.journals.uchicago.edu/doi/pdf/10.1086/708691

Model Evaluation: An Adequacy-for-Purpose View

Representation and Invariance of Scientific Structures

Astrophysics faces methodological challenges as a result of being a predominantly observation-based science without access to traditional experiments. In light of these challenges, astrophysicists ...

/pdf/observations-simulations-and-reasoning-in-astrophysics-2b7v34re97.pdf

Observations, Simulations, and Reasoning in Astrophysics

............................................................................................................................... i Acknowledgments ............................................................................................................... ii Table of

Similarity, Adequacy, and Purpose: Understanding the Success of Scientific Models

Gravitational interactions allowed astronomers to conclude that dark matter rings all luminous galaxies in gigantic halos, but this only accounts for a fraction of the total mass of dark matter bel...

The Dark Galaxy Hypothesis

Divergence of Values and Goals in Participatory Research

In philosophy, much attention has rightly been paid to the need to diversify teaching with regard to who teaches, who is taught, and which authors and questions are the focus of study. Less attention, however, has been paid to inclusive pedagogy—the teaching methods that are used, and how they can make or fail to make classes as accessible as possible to the diverse students who enter them. By drawing on experiences from our own teaching as well as research on student-centered, inclusive best practices, we advocate for five principles of inclusive pedagogy: fostering a growth mindset, examining inclusive conceptions of authority, promoting transparency, encouraging flexibility, and, finally, continually promoting self-reflection for both students and teachers.

Diversity Is Not Enough: The Importance of Inclusive Pedagogy

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