Don't bother unless you want to. I convinced myself from analyzing the Newtonian case that my 'limiting intuition' was wrong, and that if a velocity is directed in a possible escape direction, then the escape speed is not dependent on direction. The photon sphere is then analogous to a...
I haven't done the math for this, but it seems doubtful to me that at epsilon above the photon sphere, tangential escape velocity is same as radial. What I think changes for Kerr is that angle relative to spin makes a difference, as well as angle relative to radial direction.
Technical point: A flat torus cannot be smoothly embedded in Euclidean 3-space. It can be ##C^1## embedded.
A simple physical model of such an embedding is to take a paper cylinder, squash it flat, and now connect its ends. No tears or stretches involved, just 'crinkling' that suggest the...
Ah, yes. What you have are closed causal curves (e.g. two spacelike sides and a timelike side forming a causal loop). And the preferred frame restriction prevents such a construction from occurring.
Well, it is easy to have tachyons that never allow CTCs or tachyon anti-telephone, in SR. Just posit that there exists a preferred inertial frame in which all tachyon trajectories must move forward in (coordinate) time. Many people (me included) reject this on the grounds that a preferred frame...
This depends very much on what you mean by "free will" which, as you say, is clearly outside the scope of physics. In contrast, I have an argument that establishes that even if QM is taken to exclude determinism, it may well still be true that there is no free will.
The OP is correct, we don't need to consider the relative motion of B and C for the problem as posed. Each of B and C can go out and back along some straight line paths, at arbitrary angle relative to each other. Knowing that they both depart at the same time and return at the same time, but...
Note that your argument (assuming B and C are out and back along a straight line per A) elegantly proves that the angle between their paths doesn't matter. Working this out in other coordinates will be more complex, but your argument establishes that it can't matter.
To add to what @PeterDonis said, in Schwarzschild geometry, the limiting geometric elements approaching "r=0" are hypercylinders RXS2, with the S2 radius approaching 0 (this is the r=0), and the axial R being infinite in proper distance for all the elements. Each of these hypercylinders is...
This is just absurd. Lambda-DCM is described by a GR metric and nothing else - the FLRW metric family. All its physical content is contained in this full GR model. This is a theory of cosmology. There is no Lambd-CDM model of galaxy. That is a separate problem, in which dark matter is typically...
This is all mixed up. Lambd-CDM is a full GR cosmology model. There is no approximation whatsoever in all its defining equations; it is fully non-linear. To perform some types of calculations more easily, one sometimes approximates the full model in various ways. MOND has no relation to GR, it...
You misinterpret the language here. In analogy to EM, Ludwig is referring to total matter/energy currents, and the gravitic equivalent of Lorentz force. His language could be better, but his audience is assumed to understand the context. Please note the following leading sentence of the last...
That post shows no confusion about GEM having anything to do with EM fields, nor with it being any different from GR except to formulate approximate field equations in a way that shows analogy with Maxwell's equations. This is the only usage of the term I have ever seen in a published paper.
Right after the word "wrong" was a paragraph of explanation. Instead of responding to this word, perhaps respond to what you don't understand in the following explanation.
Except that most GR experts disagree with Cooperstock, and recent papers quoted in this thread cite Cooperstock and claim to rule out his claims.
FYI: I've been aware of Cooperstock's work for many years, and was initially hopeful it would work out.
In my opinion, Deur theory is an alternate gravity theory suggested by analogies between the GR Lagrangian and QCD. This is fine, except he claims that certain results are standard GR with no convincing evidence - against much evidence to the contrary ( no method starting from GR equations...
"self interaction term" has many meanings to many people. I am discussing something much more well defined. In the 4th paragraph on p. 5 of https://www.ast.cam.ac.uk/sites/default/files/Invention_DM&DE_Rev1201_011221.pdf, a term in the Einstein-Infeld-Hoffman equations (that implement first...
This paper is claimed to be thoroughly refuted by https://arxiv.org/abs/2303.06115, so the debate goes on. It establishes that the homogeneous solutions are irrelevant and endorses the Ciotti paper's conclusions.
Wrong. GEM is simply a way to write the Einstein Field Equations of GR in a way that shows analogies to Maxwell's equations. It is neither a different theory, nor does it have any relation to EM fields. It is proven to be equivalent to first order Post Newtonian approximation of GR, which is all...
I don't get what your are claiming. Even in SR, the components of a 4-vector do not stay the same after a Lorentz transform. Only scalars constructed from them stay the same.
The sugar content of the Eden mirin is remarkable given that there are no added sugars. The ingredients indicate 12 gm of sugar per 2 tbsp, none of which is added sugar. Most of the calories are from this sugar, which apparently all comes from the handling of the rice.
Well, as discussed in other threads, almost all textbooks on relativity call it norm or modulus, despite the imprecision that bothers you. Of course they know it is not a norm in the mathematical sense, but no other convenient name has caught on.
One problem with these wines is US regulations: if a wine is to be sold at a store that lacks a liquor store license, it must have salt or something similar to discourage drinking. Fortunately, there is a growing trend for grocers to have liquor licenses, but I don't know about Asian markets. In...
If you search "Hawking evaporation Kerr BH" you find a good number of reputably published papers discussing this. At the moment, I don't have time to quick read them to try to choose the most informative.
In GR, the primary definition of singularity is geodesic incompleteness. A point of spacetime where all derivatives are undefined while continuity exists must lead to geodesic incompleteness, since geodesics require satisfaction of a differential equation. So such points necessarily lead to...
But note, the Bondi energy is, by construction, not necessarily conserved even when it is well defined. The difference between the conserved ADM energy and Bondi energy is the energy of radiation (including gravitational) reaching infinity. Thus, the Bondi energy decreases for an isolated pair...
Obviously, no salt and meant for possible drinking would be better (the Eden has only 10% alcohol). But it sure seems a lot better than what you were describing. I’ve found it quite nice in cooking, but I am no expert.
Eden Mirin is readily available in Whole Foods. It is product of Japan, with ingredients water, rice, sea salt, Koji (aspergillus) and nothing else. It is traditionally brewed. Unfortunately, it does have salt.
Another criticism, also not yet published, is described in:
at around 20 minutes through the end of the video. Smethurst's primary research is in BH growth, and she finds the data analysis wholly unconvincing (she would never make such an accusation, but what I feel from her discussion is an...
That does not make sense to me. For a region of substantial size 'near' us, we are seeing 'near' current mass of BH. While high z BH are seen as they were in the past, if their present is radically different from the region around us, then homogeneity is violated, and the framework of FLRW...
One criticism I've heard from some physicists (but I don't see it published yet) is that black holes observed gravitational mass is much less than 1% of total mass per large cosmological volume. Dark Energy equation of state means pressure is the negative of gravitational mass, but it doesn't...
I broke my first bone ever playing ping pong in the style of pros (without commensurate skill) on a slippery floor. First time I realized I could not pretend to be 25 when over 70.
I'll just make the comment that the first two sentences of the abstract:
"Observations have found black holes spanning ten orders of magnitude in mass across most of cosmic history. The Kerr black hole solution is however provisional as its behavior at infinity is incompatible with an expanding...
Lemaitre also was possibly the first to demonstrate that there is no singularity or misbehavior at the horizon of a Schwarzschild (vacuum) solution, by producing the so called Lemaitre coordinates for this solutions (which are simply the Gaussian Normal coordinates).
To underscore @Vanadium 50 point, in a BH geomertry, there is singularity in the future of (all world line for Schwarzschild case; some world lines for every BH). In our universe modeled by any plausible FLRW solution vaguely matching observation, there is no singularity in the future of any...
I agree that it is likely (or at least plausible) that a few of the chess 960 starting positions are forced wins for one side.
There was a chess variant I found far more interesting than chess 960 (with prescribed starting positions and complex castling rules), that never caught on. There was...
In my OP I stated that opening position being drawn and many positions with best play from opening having multiple moves that maintain a draw were conjectures supported by experience, not proven. I wanted the thread to assume these were true, to discuss their implications, not the conjectures...
Actually, several major tournaments have banned agreed draws in chess. Theoretically, all draws are stalemate or repetition. For practical reasons, "insufficient material" is added, but it would ultimately be a draw anyway by repetitions. Similarly, the 50 move rule is added as shortcut - in...
To make one of my points concrete, I propose a class of imperfect player whose degree of imperfection is specified by a positive integer k (lower k is more imperfect). No matter the choice of k, this player would lose a sufficiently long match with a tablebase player. However, none of the...