# Time contraction. Is there a way for time to pass faster, instead of slower?

Well.. we all know about time dilation, ie time running slower. So, if you are too fast, or if you are near a blackhole. This happens. But is it possible to do the opposite? How?

We can think in the problem this way:

The Problem: Have two persons, you and your friend. You both meet (ie, for now they are in the same point of spacetime). You both decide you want to unlock the secrets of the universe. You both learn at the exactly same rate. You both schedule a future meeting to discuss what you have learned.

Your objective: In the future meeting, you must have far more knowledge than your friend.

Restrictions:

• You cannot do anything with your friend. Your friend has free will and you will respect it. Thus, you are not allowed to do anything with him.

• Also, your friend has decided to remain always non-accelerating, and far from any EM fields of gravity fields.

In other words, for you to have greater knowledge than your friend, you must somehow manage to time pass faster for you, and slower for your friend. Thus, the question is equivalent to the one in the title: Can time pass faster?

For instance, have a charged blackhole with Reissner–Nordström metric, and you are near it. $$ds^{2}=\left(1-{\frac {r_{{\mathrm {S}}}}{r}}+{\frac {r_{Q}^{2}}{r^{2}}}\right)c^{2}\,dt^{2}-\left(1-{\frac {r_{{\mathrm {S}}}}{r}}+{\frac {r_{Q}^{2}}{r^{2}}}\right)^{{-1}}dr^{2}-r^{2}\,d\Omega _{{(2)}}^{2},$$

The time dilation term here seems to suggest that, if the blackhole charge is massive, them time can actually pass faster, instead of slow down. After all, we have a $+$ sign in the charge dependent terms (time passing faster), and a $-$ sign in the mass dependent terms (time dilation, time slowing down). So.. theoretically.. if you have a huge amount of charge....

Is this correct? Can you actually make time pass faster with respect to your friend, by just being near to an insane amount of charge?

Are there other ways in physics, that time can pass faster?

• A clock (at rest) higher in a gravitational well runs faster than an identical clock (at rest) lower in the well. As always, though, when you ask "Is there a way for time pass faster...", be prepared to answer the question of faster according to whom? – Alfred Centauri Oct 22 '16 at 2:42
• @AlfredCentauri Thanks for pointing out. I think now its quite clear =). – Physicist137 Oct 22 '16 at 4:55

No, it can't happen. At least with a caveat I describe below. The calculation and logic below shows that it cannot happen if the Cosmic Censorhip Conjecture by Penrose, and accepted by most physicists as likely, that there are no naked black holes, that is black holes without horizons.

The reason it can't is because $r_Q$ can never get big enough. You can never add enough chatrge to make it so, the black hole before forming will shed any extra material so it can't become a naked black hole. You can see it by getting the expression for time dilation/contraction. To get the expression, set $\mathrm dr = \mathrm d\Omega = 0$ in the metric, so you can get the time dilation/contraction by solving for

$$\mathrm d\tau = \mathrm ds = g_{tt}c~\mathrm dt.$$

Time dilation has $g_{tt}$ < 1, since tau is the proper or observer time. t is for an observer at infinity. It turns out that always it has to be so. That expression cannot be > 1. There is nocontraction possible. Here's why.

Well, clearly the $g_{tt}$ metric term, the inverse of the $g_{rr}$ term, is zero at the horizon. It has two solutions, or one or none. You can follow the algebra in section 5.4 of the link below, if $r_s$ < $2r_Q$ there is no solution. So if that is true there is no horizon, and the Black Hole (BH) has a naked singularity. That condition that

2$r_Q$ = $r_s$ is called an extremal BH. The Q term is due to charge, the other term just to the gravitational effect proportional to G. So if you add more charge to an extremal BH it becomes a naked BH.

The Cosmic Censorship Conjecture by Penrose, not proven but with no exceptions found and generally believed to hold true (except for quantum effects, which we don't know what will do, but we do know there are quantum exceptions), is necessary for no naked singularities, and thus no non-causal possible (believed to be non-physical) spacetimes.

So, if you try to add more charge than that in an extremal BH, the BH does not allow it. If it starts collapsing with more, it sheds the extra charge, to become extremal or less.

And for all then possible BHs, under this Conjecture, you never have time contraction outside the BH, it's always time dilation.

The Kerr Newman BH also has extremal BHs and if you rotate faster it also becomes a naked singularity, also prohibited. In both cases there's been simulations and beyond extremal the Collapsing material just sheds what it needs to to never become a naked singularity. The Conjecture holds.

Note that the BH in Interstellar was pretty close to an extremal BH, but less than extremal. He (they?) aged very slowly, were years younger than their friends when they came back.

Sorry for bursting that hope. You'll have to find some other solution. Maybe there's a conjecture that you can't have time contraction unless you have a negative curvature, or a curvature significantly less than the cosmological average. Maybe the so called cosmic voids, but I believe there is uncertainty about whether they are more than statistical flukes in the data

The link for section 5.4 See the article at http://umu.diva-portal.org/smash/get/diva2:912393/FULLTEXT01.pdf

Other treatments of the metric for the Reissner Nordstrom BH at Wikipedia at https://en.m.wikipedia.org/wiki/Reissner–Nordström_metric

Try loosing weight. If you loose weight, such that your mass is less than your friend's, you will end up aging more than your friend, because he has more mass and hence more self gravity. Also, don't study from physical books as they are thick and massive and would slow down your aging relatively. Buy e-reader.