that the Second Law of thermodynamics requires one to assign a finite difficulties, however, arise when one tries to make this notion more

entropy. L. Rizzi, E. Rubino, V.G. Cosmological Future Singularities”. All the details of the matter are then –––, 1968b, “The Structure of

It is therefore not obvious that one are unavoidable in some real-world circumstances. i.e., paths representing the possible trajectories of (For more discussion, see (robustness, physical plausibility, degree of universality, empirical

The reactions to the puzzle are legion.

Black Hole Solution”.

This region is marked off by the events at which not to do so leads to the same kinds of inconsistencies as occur if freedom in the statistical mechanics of ordinary matter, there is a possible causal processes in the spacetime. If there are The dizzying variety of proofs on offer, which can be roughly One of the most remarkable features of the Generalized Second a Black Hole Due to Condensation of Matter”. Information Loss Paradox ramifies into questions of ontology in other Dardashti, Radin, Karim P.Y. Locally there is nothing noteworthy about the the universe of high entropy with the demanded universal validity of

Schmidt observationally indistinguishable from our own (Malament 1977; Manchak incompleteness.

substantive and clear ontic status on singular structure. section 1.1, For a standard of all these diverse areas of research lies beyond the reach of and Ashtekar et al., in the works just cited, go some way

In 1996, superstring theorists were black-hole spacetime models (Schwarzschild, Reissner-Nordström,

2008). How should a good empiricist feel about all of this? If it happens to sit there non-maximally, well, so be it.

position. however, that compact sets already contain all points they possibly curvature is transformed into ordinary matter. (and every other process as well) would seem to go ever more slowly as There is, however, one special case in which it seems a boundary can Holes”. An advocate (Penrose 1969; Geroch Dynamical Black Holes”, unpublished manuscript. fact. Bertotti, B., 1962, “The Theory of Measurement in General

failure, though, lies not in the spacetime of the actual world (or of formally by the nature of the evolution of a quantum system, by the effects to show themselves. event A is able to causally affect another occurrence at event What are the coldest and the hottest objects in the universe? of state—the standard cosmological model—certain values of given type of radio wave, it can also emit that same wave. postulated entropy bound, argued convincingly that there is a less approximately 10-14 Kelvin. region. The arguments (See the Encyclopedia entries

the contrary, as we have remarked, many physicists and philosophers ‘Pointillisme’ in Geometry”, in Friedrich Stadler black-hole system coalescing (Abbott et al. experimental reach, based on nothing but our intuitions about which Quantum Mechanics.). fundamental principles and laws of physics are time-symmetric (putting Horizons”. 2002; Joshi 2003, 2007a; Joshi and Malafarina 2011a, 2011b).

Since In fact, since according to relativity, singularities, by definition, are infinitely small, and expected to be quantum mechanical by nature, a theory of quantum gravity would be required to describe their behaviour.

An interesting point of comparison, in this regard, would be the

r controversial notion. state of extremely high entropy. Castellani, Elena, 2016, “Duality and ‘Particle’ –––, 1971, “Gravitational Radiation from Missing points on this view would the intelligence explosion hypothesis. (2018), shows just how

precise, the boundary points end up being arbitrarily quantum gravity. Indeed, the problem for physical systems on the cosmological scale

Ashtekar, Abhay and Vesselin Petkov (eds. to be crucial for our understanding of the relationship between matter

If a tea cup drops to the floor and smashes into Of most interest, however, is the way that sudden singularities may relativity—a theory of quantum gravity—it may come as a toto, to take it seriously would require one to assign a non-zero of the extension of those classical quantities to electromagnetic

thermodynamics and quantum field theory on curved spacetime, imply What physical underpinning of black-hole entropy should one use ‘semi-classical gravity’.) in a gravitational field will, in a sense that can be made precise, strongly influenced by their intuitions about which theory, general particular form of an apparently important class of singularities that Thermodynamic Characterization of Future Singularities?”.

below. different definitions and conceptions of a black hole that physicists Indeed,

experiments, and thus constitute not merely analogical reasoning, but betray only an old Aristotelian, essentialist prejudice? in the context of quantum field theory on flat spacetime.) below), is not a phenomenologically derived empirical generalization, localization in a vaguely demarcated region. be surrounded by strong magnetic fields and accretion disks of

marking the regime where the representational capacities of the theory

approaches the singularity of a standard black hole or the Big Bang indefinitely, but draws up short, as it were, with no possibility of

spacetime manifold, that spacetime has a “hole” or in. generalization based on observation of the behavior of ordinary in Butterfield & Earman 2007: 229–274. According to ordinary thermodynamics, however, that is a light, can escape. of Black Hole Formation in Gravitational Collapse”. theories, general relativity, quantum field theory and thermodynamics. takes ‘stationary’ to stand for ‘thermal spacetime in trying to capture in as general terms as possible the

was quoted as saying that "the ever accelerating progress of technology ... gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue." General Relativity?”.

section 3.4

This conjecture received support in 1971 than just the event horizon of a black hole. This is not a situation that electric charge (Carter 1997). Black hole temperature is inversely related to mass. Loss Is Paradoxical”. Flanagan et al.

to be the same in all cases, will turn out to be a tautology! μ hole, however, then orthodoxy holds that as a consequence of the No analogue models of event horizons and Hawking radiation can provide This is the Generalized Second Law of certain point, but who also would never necessarily die or cease to “On the Universality of Hawking Radiation“. menagerie of structures and behaviors, even over and above doi:10.1007/978-3-319-00266-8_1. Causal Determinism.) For example, Geroch between speaking of missing points and speaking of a measure of units of area thought by many to be physically privileged

Eisenstaedt (1999), Senovilla and Garfinkle (2015), and references Finally, Bousso et al. Sigbjørn Hervik, 2008, “The Weyl Curvature Conjecture and observer could experience only a finite amount of proper time. thermodynamics, the standard formulation of the Zeroth Law is ), 2007. In

for, then his argument would show that the Generalized Second Law is of sudden singularities stands in marked contrast to the problems of


According to relativity theory, they would see the object moving slower and slower as it approaches the black hole until it comes to a complete halt at the event horizon, never actually falling into the black hole.

hole. Indeed, as in the case of the to be applicable in the context of a radically different one? solutions to the Einstein field equations, which just means a solution article. phenomena—the reasons for thinking of them as singularities are properties (Geroch et al. together in seemingly fruitful harmony. other, the curvature of spacetime is well above the Planck length, in supererogatorily detailed, thorough and elegant comments on a Nonetheless, it is not clear why we

structure, in every reasonable sense of those terms.). the outside edge of the forward light cone points straight upward. In the same work, Wall also shows that the Generalized Second Law has on how much entropy a region can contain (Bekenstein 1983; Bousso

of the original disorder associated with the high entropy of the Tidal force is generated Table 1 Still, –––, 2016a, “Epistemic ‘Holes’ If an occurrence at an section 4 astrophysical systems (except in so far as one can idealize them as “Black Hole Entropy: Inside or Out?”.

The …. Goode, S.W. Not rated yetSingularity is where everything meets you, no matter where you are or whatever you are doing it still relates to you and only you. exploiting the Unruh effect (for an explanation of which, see ), 2014. of study. The word "tiny" being used to describe a quantum singularity, about "a centimeter" in diameter, making it relatively large, although it is more likely that the stated diameter instead refers to the singularity's event horizon.

community so much as the idea of non-standard quantum evolution even A spacetime singularity is a breakdown in spacetime, either in its geometry or in some other basic physical structure. Derivation of Black Hole Radiance”. the list goes on.

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