Narrow Results

We discuss the macroscopic quantum tunneling from the black hole to the white hole of the same mass. Previous calculations in [G. E. Volovik, Universe 6, 133 (2020)] demonstrated that the probability of the tunneling is $p\propto exp(-2S_{\mathrm{\text{BH}}})$, where $S_{\mathrm{\text{BH}}}$ is the entropy of the Schwarzschild black hole. This in particular suggests that the entropy of the white hole is with minus sign the entropy of the black hole, $S_{\mathrm{\text{WH}}}(M)=-S_{\mathrm{\text{BH}}}(M)=-A/(4G)$. Here, we use a different way of calculations. We consider three different types of the hole objects: black hole, white hole and the fully static intermediate state. The probability of tunneling transitions between these three states is found using singularities in the coordinate transformations between these objects. The black and white holes are described by the Painleve–Gullstrand coordinates with opposite shift vectors, while the intermediate state is described by the static Schwarzschild coordinates. The singularities in the coordinate transformations lead to the imaginary part in the action, which determines the tunneling exponent. For the white hole the same negative entropy is obtained, while the intermediate state — the fully static hole — has zero entropy. This procedure is extended to the Reissner–Nordström black hole and to its white and static partners, and also to the entropy and temperature of the de Sitter Universe.

This paper examines the interaction of an intense fermion field with all of the particle species of an attometer primordial black hole’s (PBH) high energy Hawking radiation spectrum. By extrapolating to Planck-sized PBHs, it is shown that although Planck-sized PBHs closely simulate the zero absorption requirement of white holes, the absorption probability is not truly zero, and therefore, thermodynamically, Planck-sized primordial black holes are not true white holes.

In this paper, the structure of the generalized Vaidya space–time when the type-II of the matter field satisfies the equation of the state $P=\rho$ is investigated. Satisfying all energy conditions, we show that this space–time contains the “eternal” naked singularity. It means that once the singularity is formed it will never be covered with the apparent horizon. However. in the case of the apparent horizon formation the resulting object is a white hole. We also prove that this space–time contains only null naked singularity.

A central idea in general relativity is that physics should not depend on the spacetime coordinates in use [A. Einstein, The Meaning of Relativity (Princeton University Press, 1945)]. But the qualitative description of various phenomena can appear superficially quite different. Here, we consider falling into a classical black hole using four distinct but equivalent metrics. First is the Schwarzschild case, with extreme time dilation at the horizon. Second, rescaling the dilation allows falling into the hole in finite proper time. Third, time and space are rescaled into a Penrose motivated picture where light trajectories all have unit slope. Fourth, a white hole variation of the second metric allows passage out through the horizon, with reentry forbidden.

We derive and analyze the equations that extend the results in [20,21] to the case of non-critical expansion k≠0. By an asymptotic argument we show that the equation of state plays the same distinguished role in the analysis when k≠0 as it does when k=0: only for this equation of state does the shock emerge from the Big Bang at a finite nonzero speed — the speed of light. We also obtain a simple closed system that extends the case considered in [20,21] to the case of a general positive, increasing, convex equation of state p=p(ρ).