Rigor:

     Rigor mortis is a key indicator used by forensic experts to estimate the time of death. It refers to the stiffening of the body's muscles that occurs after death, caused by chemical changes in the muscle tissue.

The process of rigor mortis follows a predictable timeline:
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- Immediately after death, the muscles are relaxed.
- Over the next 2-3 hours, rigor mortis begins to set in, starting with the smaller muscles of the face, neck, and hands.
- It then progresses to the larger muscle groups over the next 6-12 hours, until the entire body is in a state of full rigor mortis.
- Rigor mortis typically peaks and remains fully developed for another 12 hours.
- After 24-36 hours, the rigor mortis begins to subside as the muscles relax again
- When rigor is broken after maximal development, it usually doesn’t reappear.

The duration and progression of rigor mortis can provide important clues about the time of death:

- If the body is not stiff but there is evidence rigor mortis has already passed, it suggests the death occurred more than 36 hours ago.
- If rigor mortis is just beginning to set in, it indicates the death occurred within the past 2-3 hours.
- If the body is in full rigor mortis, it typically means the death occurred 6-12 hours prior.
- The reappearance of rigor mortis after it has been broken can suggest the death occurred less than 8 hours ago.

However, it's important to note that the rate of rigor mortis development can be affected by various factors:

- Temperature - Warmer temperatures speed up the process, while cooler temperatures slow it down.
- Physical activity before death - Increased muscle activity leads to faster rigor mortis.
- Underlying medical conditions - Certain illnesses that increase acidity in the muscles can accelerate rigor mortis.
- Manipulation of the body - If the body is moved or positioned after rigor mortis has set in, it can disrupt the process.

     So while rigor mortis is a valuable tool, forensic experts must consider these variables when using it to estimate time of death. It is not an exact science, but rather provides a general timeframe that can be refined with other evidence.

Livor:

     Livor mortis, also known as post-mortem lividity or hypostasis, refers to the pooling of blood in the lower, dependent parts of the body after death. This results in a characteristic purple-red discoloration of the skin.

The progression of livor mortis follows a predictable timeline:

- Livor mortis begins to appear as dull red patches 20-30 minutes after death.
- Over the next 2-4 hours, these patches expand and darken into larger areas of bluish-purple discoloration.
- For the first 8-12 hours, the skin is "blanchable" - meaning the discolored areas will temporarily turn white when pressure is applied, then return to the purple color.
- After 12 hours, the livor mortis becomes "fixed" or non-blanchable, as the blood pools into the tissues and can no longer be displaced by pressure.
- Maximum/fixed lividity is typically reached 8-12 hours after death

Forensic experts can use the progression of livor mortis to help estimate the time of death:

- If the body is found and the skin discoloration is still blanchable, it suggests death occurred within the past 12 hours.
- If the livor mortis is fully fixed and non-blanchable, it indicates the death likely occurred more than 12 hours ago.
- The location and pattern of livor mortis can also reveal if the body has been moved after death, as the pooling will be in the dependent areas at the time of death. Contact pallor occurs when blood is pushed out of areas that come in contact with surfaces/objects.
- The color of the livor mortis can provide clues about the cause of death, such as a reddish hue in carbon monoxide poisoning.

     Livor mortis is not an exact science for determining time of death. Factors like temperature, body position, and underlying medical conditions can all affect the rate and appearance of livor mortis. Forensic experts typically use livor mortis in conjunction with other indicators like rigor mortis and algor mortis to provide a more accurate estimate.

Algor:

     Algor mortis, or "cold death", refers to the decrease in body temperature that occurs after death. This happens as the body loses its ability to regulate its own temperature.

The progression of algor mortis follows a predictable pattern:

- Immediately after death, the body temperature begins to drop.
- For the first 1-2 hours, the body temperature decreases at a rate of about 1.5°C (2.7°F) per hour.
- After the initial rapid cooling, the rate of temperature decrease slows to about 1°C (1.8°F) per hour.
- This gradual cooling continues until the body reaches the ambient temperature of the surroundings

Forensic experts can use the rate of algor mortis to estimate the time of death:

- By measuring the current body temperature and knowing the ambient temperature, they can calculate the time elapsed since death using the Glaister equation:

          - Time since death (hours) = (36.9°C - body temperature in °C) × 6/5
          - Time since death (hours) = (98.4°F - body temperature in °F) / 1.5

- However, this formula assumes a normal starting body temperature of 36.9°C (98.4°F) and a constant cooling rate, which is not always the case.
- Factors like clothing, body size, and environmental temperature can all affect the rate of cooling and make the time of death estimate less accurate. Particularly in climates like the Arizona heat, or the Alaskan snow, Algor mortis becomes less and less predictable.

     It's important to note that algor mortis is not a standalone method for determining time of death. Forensic experts typically use it in conjunction with other indicators like livor mortis and rigor mortis to provide a more reliable estimate. The accuracy of algor mortis-based time of death calculations can also be improved by using more complex mathematical models that account for additional variables.