Falling into the Schwarzschild black hole. Important details

The Schwarzschild space is one of the best studied spacetimes and its exhaustive considerations are easily accessible. Nevertheless, by some reasons it is still surrounded by a lot of misconceptions, myths, and "paradoxes". In this pedagogical paper an attempt is made to give a simple (i. e., without cumbersome calculations), but rigorous consideration to the relevant questions. I argue that 1) an observer falling into a Schwarzschild black hole will \emph{not} see "the entire history of the universe" 2) he will \emph{not} cross the horizon at the speed of light 3) when inside the hole, he will \emph{not} see the (future) singularity and 4) the latter is \emph{not} "central".Comment: v1. In Russian v.2 Replaced by the English versio

Counter example to a quantum inequality

A `quantum inequality' (a conjectured relation between the energy density of a free quantum field and the time during which this density is observed) has recently been used to rule out some of the macroscopic wormholes and warp drives. I discuss the possibility of generalizing that result to other similar spacetimes and first show that the problem amounts to verification of a slightly different inequality. This new inequality \emph{can} replace the original one, if an additional assumption (concerning homogeneity of the `exotic matter' distribution) is made, and \emph{must} replace it if the assumption is relaxed. Then by an explicit example I show that the `new' inequality breaks down even in a simplest case (a free field in a simply connected two dimensional space). Which suggests that there is no grounds today to consider such spacetimes `unphysical'.Comment: Sec. II is completely rewritten: the gulf is discussed between the proven QIs and those used in ruling out exotic spacetime

Paradoxes of time travel

Paradoxes that can supposedly occur if a time machine is created are discussed. It is shown that the existence of trajectories of ``multiplicity zero'' (i.e. trajectories that describe a ball hitting its younger self so that the latter cannot fall into the time machine) is not paradoxical by itself. This {\em apparent paradox} can be resolved (at least sometimes) without any harm to local physics or to the time machine. Also a simple model is adduced for which the absence of {\em true} paradoxes caused by self-interaction is proved.Comment: 9 LaTeX pages, 23k. bezier.sty is desirable, but its absence will only damage two figure

What is faster -- light or gravity?

General relativity lacks the notion of the speed of gravity. This is inconvenient and the present paper is aimed at filling this gap up. To that end I introduce the concept of the "alternative" and argue that its variety called the "superluminal alternative" describes exactly what one understands by the "superluminal gravitational signal". Another, closely related, object called the "semi-superluminal alternative" corresponds to the situation in which a massive (and therefore gravitating) body reaches its destination sooner than a photon \emph{would}, be the latter sent \emph{instead} of the body. I prove that in general relativity constrained by the condition that only globally hyperbolic spacetimes are allowed 1) semi-superluminal alternatives are absent and 2) under some natural conditions and conventions admissible superluminal alternative are absent too.Comment: A few minor additions mor

Finite energy quantization on a topology changing spacetime

The "trousers" spacetime is a pair of flat 2D cylinders ("legs") merging into into a single one ("trunk"). In spite of its simplicity this spacetime has a few features (including, in particular, a naked singularity in the "crotch") each of which is presumably unphysical, but for none of which a mechanism is known able to prevent its occurrence. Therefore it is interesting and important to study the behavior of the quantum fields in such a space. Anderson and DeWitt were the first to consider the free scalar field in the trousers spacetime. They argued that the crotch singularity produces an infinitely bright flash, which was interpreted as evidence that the topology of space is dynamically preserved. Similar divergencies were later discovered by Manogue, Copeland and Dray who used a more exotic quantization scheme. Later yet the same result obtained within a somewhat different approach led Sorkin to the conclusion that the topological transition in question is suppressed in quantum gravity. In this paper I show that the Anderson--DeWitt divergence is an artifact of their choice of the Fock space. By choosing a different one-particle Hilbert space one gets a quantum state in which the components of the stress-energy tensor (SET) are bounded in the frame of a free-falling observer.Comment: v.2 The zeroth mode is abandoned. The presentation is simplified and clarified v.3 Title has changed. A few typos are corrected, et

No to censorship! Comment on the Friedman-Schleich-Witt theorem

I show that there is a significant lacuna in the proof of the theorem known as "Topological Censorship" (a theorem forbidding a solution of Einstein's equations to have some topological features, such as traversable wormholes, without violating the averaged null energy condition). To fill the lacuna one would probably have to revise the class of spacetimes for which the theorem is formulated.Comment: 6 negative reviews! Most idiotic ones may be sent upon reques

The wormhole hazard

To predict the outcome of (almost) any experiment we have to assume that our spacetime is globally hyperbolic. The wormholes, if they exist, cast doubt on the validity of this assumption. At the same time, no evidence has been found so far (either observational, or theoretical) that the possibility of their existence can be safely neglected.Comment: Talk given at "Time and Matter", Venice 200

Schwarzschild-Like Wormholes as Accelerators

In a stationary spacetime $S$ consider a pair of free falling particles that collide with the energy $E_{\rm c.m.}$ (as measured in the center-of-mass system). Let the metric of $S$ or/and the trajectories of the particles depend on a parameter $k$. Then $S$ is said to be a "(super) accelerator" if $E_{\rm c.m.}$ grows unboundedly with $k$, even though the energies of the particles at infinity remain bounded. The existence of naturally occurring super accelerators would make it possible to observe otherwise inaccessible phenomena. This is why in recent years a lot of spacetimes were tested on being super accelerators. In this paper a wormhole $W$ of an especially simple---and hence, hopefully, realistic---geometry is considered: it is static, spherically symmetric, its matter source is confined to a compact neighbourhood of the throat, and the $tt$-component (in the Schwarzschild coordinates) of its metric has a single minimum. It is shown that such a wormhole is a super accelerator with $k\equiv \frac 13\ln |g_{tt\ \mathrm{min}}|$. In contrast to the rotating Teo wormhole, considered by Tsukamoto and Bambi, $W$ cannot accelerate the collision products on their way to a distant observer. On the other hand, in contrast to the black hole colliders, $W$ does not need such acceleration to make those products detectable.Comment: A few corrections, and clarifications. 2 graphs are adde

Time machine (1988--2001)

A very brief and popular account of the time machine problem.Comment: Talk given at 11th UK Conference on the Philosophy of Physics (Oxford 2002

Yet another proof of Hawking and Ellis's Lemma 8.5.5

The fact that the null generators of a future Cauchy horizon are past complete was proved first by Hawking and Ellis [1]. Then Budzy\'nski, Kondracki, and Kr\'olak outlined a proof free from an error found in the original one [2]. Finally, a week ago Minguzzi published his version of proof [3] patching a previously unnoticed hole in the preceding two. I am not aware of any flaws in that last proof, but it is quite difficult. In this note I present a simpler one.Comment: A few misleading typos are correcte