← Back to article

Equation 27 · How Fast Can a Horizon Learn Which Path You Took?

What does this equation mean?

V(T)=exp⁡ ⁣(−CκT2),V(T)=\exp\!\left(-\frac{C\kappa T}{2}\right),

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

Start withCkappa T
Divide by2
This relates toV(T)
How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

VV

Symbol V

V is part of the quantity the equation computes from the expression on the right.

Understand this part →

TT

Symbol T

the associated Killing time.

Understand this part →

CC

Symbol C

their dimensionless decohering flux.

Understand this part →

κ\kappa

Symbol kappa

surface gravity with inverse-time units in the chosen normalization.

Understand this part →

=

=

The expressions on both sides represent the same quantity under the stated assumptions.

Understand this part →

See an illustrated explanation →
fraction

fraction

Divide the expression above the line by the one below it.

Understand this part →

See an illustrated explanation →
CκTC\kappa T

Numerator: Ckappa T

The complete quantity above the fraction bar.

Understand this part →

22

Denominator: 2

The complete quantity below the fraction bar; it must be nonzero for this division.

Understand this part →

How to interpret it

With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

Gralla and Wei calculate the large-holding-time overlap for nonextremal bifurcate Killing horizons in electromagnetic and Klein–Gordon analogues. In their natural-unit convention, V(T)=exp⁡ ⁣(−CκT2)V(T)=\exp\!\left(-\frac{C\kappa T}{2}\right). so the adapter into the exponential ledger is

Read the equation in its article →

Sources cited in the article section

These citations give research context. Read each source to check which claims it supports.

Return to How Fast Can a Horizon Learn Which Path You Took?

See this formula across 1 published context →

Browse the mathematical compendium →